On Mon, Jun 15, 2015 at 9:04 AM, YKY (Yan King Yin, 甄景贤) <
[email protected]> wrote:

>
>
> I found out that a "distributive representation"​
>
> ​does not come with superposition (I don't recall where I got that idea
> from).
>
> For example, 100 neurons which take only binary (0,1) values can represent
> maximally 2^100 different "states".  This is vastly bigger than the number
> of states for a completely local representation, which would be 100.
>
> But now we have no way to superimpose the states -- all the available bits
> are used up.
>
> ​I have to research a bit about the idea of superposition...  to see how
> it gels with distributive representations.
>
> PS:  if we use a dimension higher than the dimension of the signal, that
> representation is called "over-complete", and mathematically it's called a
> "frame" (the famous example being the "Mercedes Benz"​ tri-vector "basis"
> for 2-D space).
> There are ways to use such representations to increase accuracy or combat
> noise.
>



Could you explain this a little more. I found references but I could not
really get what you are getting at. For example, are any multiple vectors
used as a "basis" then "over-complete" and called a "frame"? What does it
mean to use multiple vectors as a basis? How is that useful? Would they be
used to increase accuracy because of round off errors (like taking multiple
readings to determine the position of a broadcast from a boat) or are you
talking about something else?
Jim Bromer



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